Bilbao Crystallographic Server arrow Wyckoff Sets: Equivalent Sets of Wyckoff Positions

Wyckoff Sets of Space Group Pcc2 (No. 27)

NOTE: The program uses the default choice for the group settings.

Letter Mult SS Rep. Equivalent WP under
Euclidean normalizer		 Equivalent WP under
affine normalizer
e 4 1 (x, y, z) e e
d 2 ..2 (1/2 , 1/2 , z) abcd abcd
c 2 ..2 (1/2 , 0, z) abcd abcd
b 2 ..2 (0, 1/2 , z) abcd abcd
a 2 ..2 (0, 0, z) abcd abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Pcc2 (027) under the coset representatives of its affine normalizer


Index: 16 · (∞)

No. # Coset Representative Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
 
a b c d e
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
c d a b e
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
b a d c e
4x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
d c b a e
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
 
a b c d e
6-x+1/2,-y,-z
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)
 
c d a b e
7-x,-y+1/2,-z
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1    0
)
 
b a d c e
8-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
 
d c b a e
9y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a c b d e
10y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
b d a c e
11y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
c a d b e
12y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
d b c a e
13-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
 
a c b d e
14-y+1/2,-x,-z
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1    0
)
 
b d a c e
15-y,-x+1/2,-z
(
   0  -1   0    0
  -1   0   0   1/2
   0   0  -1    0
)
 
c a d b e
16-y+1/2,-x+1/2,-z
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1    0
)
 
d b c a e




Additional traslations generators


No. # Continuous Translations Transformed WP
1 x,y,z+t
(
   1   0   0    0
   0   1   0    0
   0   0   1    t
)
 
a b c d e


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